If memory serves the Sonic stuff was emulated anyway and that was why it was not great.

Anyway yes a better flash cart can but most things you find will run at about native/original speed anyway. Faster memory can help but the main things that change what you see is anti piracy removal can speed things up (mainly in things like scrolling through a long menu), also some flash carts improved a few things.
Stuff like Castlevania portrait of ruin crashing/speed fixes was more of a latency thing and bad programming on the part of the devs of the game, such things having since been fixed.

The onboard processors do nothing for this as they are only for the extra features and homebrew.